@CoAndy What do you want to use your card for? Are you just going to get it for eShop games, or for retail downloads?
All you have to do to transfer from one card to the other is put your SD card into your computer, copy all the files into an empty folder, place the new card in, and copy the data into the new SD card. Just don't delete the files on the original SD card until you know 100% the transfer worked. Keep the files on your computer as back-up as well just in case.

"The Nintendo 3DS is compatible with SD cards up to 2GB in size, and SDHC cards of 4GB and larger.
MiniSD and MicroSD cards are compatible with the use of an SD Card Adapter."

I hear the SanDisk 32GB microSD Memory Card being recommended a lot. I personally use a 16GB HP microSD Memory Card, although I'm probably going to upgrade to the bigger 32GB size soon. I've heard you can make cards up to 128GB work with the 3DS if you re-format them, but I doubt anybody needs that much memory.

As to the procedure....
Put your SD Card or adapter into a SD Card slot in your PC.
Copy the files from your SD Card to a folder on your desktop
Copy the files from the desktop folder to the new SD Card
Put your new SD Card in your 3DS

One change from @Ralizah's recommendation - I'd just get a regular 32GB SDHC Card as opposed to dealing with a microSD and a converter. Just seems like less of a hassle to use a regular card when they're as plentiful as microSDs.

I just used the SanDisk 32 GB one mind you not the extreme series and it oddly works. I had no issues with it and everything I downloaded with it gave me no errors and stuff.

But seriously why can't Nintendo instead make their own SD Cards and sell those to us instead? It would make a whole lot more sense than scratching your head figuring out from others which SD card works

@ArtWark Its bad enough buying Sony's own Cards for their Vita that can cost £100. Besides, finding a good SD Card isn't hard work, just stick to SanDisk. Is it really that hard? Also, everyone has hundreds of SD Cards in their draws somewhere.

The high data transfer rate is probably what you would want to look for if you get an SD card over 32GB. This Sony card has 40mbs transfer speed, but I'm not entirely sure if that's the main factor for making sure an SDXC card works in FAT32. I would guess very strongly that it does, but again, I'm not entirely sure.